Modeling, inference and risk aggregation for dependent insurance losses

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Insurance companies are now increasingly interested in the detailed modeling of their policies and claims. At such level of granularity, dependence between the different components naturally arises, and must be considered to appropriately measure the overall risk. My research program focuses on the development of sound models and statistical methods to account for dependence between general insurance risks. Copula-based models are more adequately representing the dependence in multivariate data than the usual multivariate distributions. They are formed by a copula, encapsulating the dependence structure, and a marginal distribution for each of the random variable. However, high-dimensional versions of common copulas are often too restrictive in practice, and my research program aims at providing new options of flexible copulas that are interpretable through a stochastic representation. Hierarchical constructions generalizing the background risk model, which is basically a random scaling applied to a random vector, will lead to dependence structures that may exhibit asymmetries, homogeneous subvectors and have different levels of lower and upper tail dependence. I will also develop the corresponding inference procedures. As big data analysis is changing the game in the insurance industry, I will study copula models in conjunction with complex, hard-to-interpret marginal distributions built from machine learning procedures that are now available to improve the fit. The models and the corresponding inference procedure that I will develop could be applied in actuarial, hydrological or financial applications and I will make them accessible through the R Project for Statistical Computing. In a micro-level reserving framework, upon the reporting of a claim and throughout its payment process until settlement, the insurer holds a reserve to cover for the future amounts to be paid in relation to that individual claim. I will develop tools to verify or refute the assumption of independence between the claims, which is underlying individual reserving models. When a claim involves many claimants or coverages, a dependence model is needed, and I will develop an inference procedure accounting for open and closed claims in this context. This detailed modeling is intricate, but its implementation would lead to many benefits for the insurance company, and ultimately for the Canadian insurance industry and for the customers. Examples include an improved fraud detection and early identification of costly files, a reduction in claims adjuster fees and the uncovering of changes in the claim mix or the repayment process.